The Geometry of Spacetime

Rating:
Summary: Beautiful Book
Review: After long reflection, I am convinced that this book is the most finely crafted piece of teaching I have ever encountered. If you have hard interest in relativity, spacetime, cosmology, but lack facility with mathematics more advanced than calculus and linear algebra, Callahan will lead you into a deeper understanding of the mathematics than you would have believed possible.

Rating:
Summary: this book
Review: At times this book can be confusing, often the author will make something unclear by leaving out a simple sentence or two. I can't really compare it to other texts- although i've looked through many this is the first I tried to actually learn from, but as far as a textbook goes it's not the greatest. In many places once you figure what he's trying to say, you also realize that an added sentence or step or justification would've made it far easier to understand.

Rating:
Summary: this book
Review: At times this book can be confusing, often the author will make something unclear by leaving out a simple sentence or two. I can't really compare it to other texts- although i've looked through many this is the first I tried to actually learn from, but as far as a textbook goes it's not the greatest. In many places once you figure what he's trying to say, you also realize that an added sentence or step or justification would've made it far easier to understand.

Rating:
Summary: Excellent Introduction to General Relativity
Review: I have not had a chance to work through the whole book yet, but I think the previous reviewer is correct - it is an excellent book. I particularly like the approach in the early chapters where special relativity is treated with the basic linear algebra of linear transformations. This gives several interesting applications that students often don't see early in their mathematical career.

The later chapters cover the geometry of surfaces and general relativity. I would like to learn GR in a "coordinate-free" fashion, but Callahan does not take that approach (and gives his reasons clearly in the introduction). In scanning over the later chapters it looks like the coordinate approach is balanced with lots of physical and geometric explanation.

Rating:
Summary: At Last
Review: I have spent a ton of money over the years trying to buy a book that I could learn relativity from. This is it. Although I have only worked my way through the first 3 chapters at this point, these three chapters are worth the price of the book. The subject is presented in a geometrical fashion, and up until the end of chapter 3, I have not been buried in an avalanche of subscripts. Having glanced at later chapters, I know that the subscripts and superscripts are coming, but I also believe that I will be prepared for them when they arrive.

Well done.
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Added in May 2004

I have now taught quite a few readings from this book and will be teaching a course from it this summer. It is wonderful.

Rating:
Summary: Disappointing
Review: I've only read the first third in detail, but so far this book is frankly disappointing. The treatment is lightweight and padded out with verbiage, some of it oddly off-key. What math or physics student at this level needs (for example) an elementary account of the properties of hyperbolic functions? Spacetime diagrams are drawn with the time axis horizontal, which is something I've never seen in any other relativity text. Okay, it's a minor point, but I found this and similar nonstandard usages a constant irritant. More seriously, the development of relativistic momentum and covariance in chap.3 is quite incoherent, and the definition of 4-velocity is WRONG (at least, by everyone else's standards - it isn't even a 4-vector). There are plenty of exercises, which is good, but no solutions at all - not even outlines - which is not so good.

The book takes over three hundred pages to get to general relativity (where there seems to be no mention of the equivalence principle!), and I doubt if it's worth the effort. You would do better to work through Foster & Nightingale's 'Short Course in General Relativity', which is a first-rate and accessible introduction if you have a little background in special relativity. And it's two-thirds the price.

Conclusion: There may be a good book waiting to be written on these lines, but I'm sorry to say this isn't it. I wouldn't recommend it to anyone as a first course in relativity.

Rating:
Summary: Great for learning how to actually use the math behind GR
Review: This book is great for teaching the math behind GR using excellent examples from Math and Physics problems (for another great problem solver see also Schaum's Outline of Tensor Calculus, but this has less Physics). It is a bit long winded, spending alot of time on SR and in some place just over the top (for Physicists!), but once through it there should be no problem going to the more advanced texts which deal with more of the uses of GR. At the same level I would also recommend Schutz's First Course in GR, however, Callahan's book goes through and explains the use of the math better, whereas Schutz's is better for uses in GR, surprisingly this is the strength of Callahan's book: you can't really do the Physics properly unless you can do the math! After this it's on to more Physics orientated books like Carroll's excellent Introduction to GR, as a stepping stone to MTW's Gravitation and Wald's GR.

Rating:
Summary: One of the best.
Review: This is one of the best introduction to General Relativity. It is the most accessible introduction to differential geometry. Naturally you have to know calculus, linear algebra, and the basics of special relativity. I bought many books on the subject, and this one belengs to the set I suggest for self-learning.